Problem: A pitcher's arm rotates at a speed of $7$ degrees per millisecond $\left( \dfrac{\text{degrees}}{\text{ms}} \right)$. At what speed does the pitcher's arm rotate in $\dfrac{\text{degrees}}{\text{s}}$ ?
Explanation: We will convert $7\,\dfrac{\text{degrees}}{\text{ms}}$ to a rate in $\dfrac{\text{degrees}}{\text{s}}$ using the following conversion rate: There are $1000\text{ ms}$ per $1\text{ s}$. $\begin{aligned} &\phantom{=} \dfrac{7 \text{ degrees}}{1\text{ ms}} \cdot\dfrac{1000\text{ ms}}{1\text{ s}} \\\\ &=\dfrac{7 \cdot 1000 \cdot\text{degrees}\cdot\cancel{\text{ms}} }{1\cdot 1\cdot\cancel{\text{ms}} \cdot \text{s}} \\\\ &=\dfrac{7000}{1}\,\dfrac{\text{degrees}}{\text{s}} \\\\ &=7000\,\dfrac{\text{degrees}}{\text{s}} \end{aligned}$ In conclusion, the acceleration rate in $\dfrac{\text{degrees}}{\text{s}}$ is: $7000\,\dfrac{\text{degrees}}{\text{s}}$